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Divide a 5-inch line into two parts so that one part (a) 2 1/4 inches shorter than the other; (b) 3 times the other.

Sagot :

part a), solve this system of equations:
x + y = 5
x - y = 2.25
2x = 7.25
x = 3.625
y = 1.375

part b), solve this system of equations:
x + y = 5
x = 3y
y = 1.25
x = 3.75

Answer:

We have to divide 5-inch line into two parts so that one part (a) 2 1/4 inches or 2.25 inches shorter than the other; (b) 3 times the other

We can write this statement as :

(a) [tex]x+(x-2.25)=5[/tex]

Solving this we get

[tex]2x=5+2.25[/tex]

[tex]2x=7.25[/tex]

x = 3.625 inches

And the other part will be = [tex]5-3.625=1.375[/tex] inches

(b) As we have x+y=5

We have to find two parts where one is 3 times the other. This means we have to find x=3y

So, we have [tex]3y+y=5[/tex]

[tex]4y=5[/tex]

y = 1.25 inches

Other part x is [tex]5-1.25=3.75[/tex] inches